Viscous creep in room-dried unconsolidated Gulf of Mexico shale (II): Development of a viscoplasticity model

Laboratory creep experiments show that compaction of dry Gulf of Mexico shale is a permanent irrecoverable process associated with viscoplastic deformation. In order to find a relatively simple model that can describe such viscoplastic behavior of the dry frame of the shale, we combined the Perzyna viscoplasticity constitutive law with a modified Cambridge clay plastic yield model. The constitutive equation for this model is a power-law function that relates strain rate to the ratio of dynamic and static yield surfaces defined by the modified Cam-clay model. By incorporating the effect of strain hardening on the static yield pressure, we derived an equation relating volumetric creep strain at a constant hydrostatic pressure level to the logarithm of time, which is in good agreement with experimental results. We determined the model parameters by fitting experimental data of creep strain as a function of time. The determined parameters indicate that the yield stress of the hydrostatically loaded shale increases by 6–7% as strain rate rises by an order of magnitude. This demonstrates that the laboratory-based prediction of yield stress (as well as porosity) may be significantly overestimated. Thus, strain-rate calibration is required for weak shales such as those studied here to appropriately estimate physical properties under in situ conditions.